Combined Filtering and Parameter Estimation for Discrete-Time Systems Driven by Approximately White Gaussian Noise Disturbances

Runggaldier WJ & Visentin C (1987). Combined Filtering and Parameter Estimation for Discrete-Time Systems Driven by Approximately White Gaussian Noise Disturbances. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-87-060

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Abstract

In the problem of combined filtering and parameter estimation one considers a stochastic dynamical system whose state x_t is only partially observed through an observation process y_t. The stochastic model for the process pair (x_t, y_t) depends furthermore on an unknown parameter theta. Given an observation history of the process y_t, the problem then consists in estimating recursively both the current state x_t of the system (filtering) as well as the value theta of the parameter (Bayesian parameter estimation).

The problem is a rather difficult one: Even if, conditionally on a given value of theta, the process pair (x_t, y_t) satisfies a linear-Gaussian model so that the filtering problem for x_t can be solved via the familiar Kalman-Bucy filter; when theta is unknown, the problem becomes a difficult nonlinear filtering problem.

The present paper, partly based on previous joint work of one of the authors, makes a contribution towards the solution of this problem in the case of discrete time and of a (conditionally on theta) linear model for x_t, y_t. The solution that is obtained is shown to be robust with respect to small variations in the a priori distributions in the model, in particular those of the disturbances.

Item Type: Monograph (IIASA Working Paper)
Research Programs: Adaption and Optimization (ADO)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:58
Last Modified: 23 Jul 2016 11:30
URI: http://pure.iiasa.ac.at/2992

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